Cohomogeneity one manifolds with positive Ricci curvature
160 citations recorded by the source corpus.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/dc298309dce02c34889f2af1086c666e9660d35d
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In Applied Mathematics
- W. Ziller
- Burkhard Wilking
- Wilderich Tuschmann
- Lorenz Schwachhöfer
- Yu. G. Nikonorov
- Zizhou Tang
- Christoph Böhm
- Jianquan Ge
In Geometry and Topology
- W. Ziller
- Burkhard Wilking
- Wilderich Tuschmann
- Lorenz Schwachhöfer
- Yu. G. Nikonorov
- Zizhou Tang
- Christoph Böhm
- Jianquan Ge
Citations in the corpus
- Examples of Riemannian Manifolds with non-negative sectional curvature (2007, background): “We mention that in the case of Ricci curvature one has the positive result that every cohomogeneity one manifold carries an invariant metric with non-negative Ricci curvature, and with positive Ricci curvature if and only if the fundamental group is finite [43].”
- Metrics of positive Ricci curvature on quotient spaces (2003, methodology): “Any closed cohomogeneity one manifold admits invariant metrics of nonnegative Ricci curvature ([ GZ2 ]) and metrics of almost nonnegative sectional curvature ([ST]).”
- Killing vector fields of constant length on Riemannian manifolds (2006, background): “Extensive information and bibliography on Riemannian manifolds of cohomogeneity 1 one can find in [1] and [22].”
- Isoparametric functions and exotic spheres (2010, background): “ corresponding isoparametric functions with all orbits as their level sets are proper. Proof. The desiring conclusions follow directly from the G-invariance of the Riemannian metric (see also [TT72], [GZ02]). In fact the corresponding isoparametric functions could be defined by taking composition of ”
- Nonnegatively Curved Manifolds with Finite Fundamental Groups Admit Metrics with Positive Ricci Curvature (2007, background): “Grove and Ziller [ GZ ] showed that any compact cohomogeneity one manifold with finite fundamental group admits invariant metrics with positive Ricci curvature.”